100 citations · 204 across the 32 of their papers we have counts for
33 papers
Hierarchical Clustering of Networks via Hierarchical Distance Matrices
Li Chen, Nathaniel Josephs, Eric D. Kolaczyk +1
Clustering populations of networks while recovering their latent hierarchical organization is a fundamental yet largely unexplored problem in network analysis. To formalize this, w…
Schreier-Coset Graph Rewiring
Aryan Mishra, Randy Martinez, Lizhen Lin
The information flow in the graph neural networks (GNNs) is fundamentally constrained by over-squashing, where structural bottlenecks impede long range information propagation. Gra…
Posterior Contraction Rates for Sparse Kolmogorov-Arnold Networks in Anisotropic Besov Spaces
Jeunghun Oh, Kyeongwon Lee, Jaeyong Lee +1
We study posterior contraction rates for sparse Bayesian Kolmogorov-Arnold networks (KANs) over anisotropic Besov spaces, providing a statistical foundation of KANs from a Bayesian…
Nested stochastic block model for simultaneously clustering networks and nodes
Nathaniel Josephs, Arash A. Amini, Marina Paez +1
We introduce the nested stochastic block model (NSBM) to cluster a collection of networks while simultaneously detecting communities within each network. NSBM has several appealing…
A Bayesian sparse factor model with adaptive posterior concentration
Ilsang Ohn, Lizhen Lin, Yongdai Kim
In this paper, we propose a new Bayesian inference method for a high-dimensional sparse factor model that allows both the factor dimensionality and the sparse structure of the load…
Machine Learning and the Future of Bayesian Computation
Steven Winter, Trevor Campbell, Lizhen Lin +2
Bayesian models are a powerful tool for studying complex data, allowing the analyst to encode rich hierarchical dependencies and leverage prior information. Most importantly, they…
A Semi-Bayesian Nonparametric Estimator of the Maximum Mean Discrepancy Measure: Applications in Goodness-of-Fit Testing and Generative Adversarial Networks
Forough Fazeli-Asl, Michael Minyi Zhang, Lizhen Lin
A classic inferential statistical problem is the goodness-of-fit (GOF) test. Such a test can be challenging when the hypothesized parametric model has an intractable likelihood and…
Intrinsic and extrinsic deep learning on manifolds
Yihao Fang, Ilsang Ohn, Vijay Gupta +1
We propose extrinsic and intrinsic deep neural network architectures as general frameworks for deep learning on manifolds. Specifically, extrinsic deep neural networks (eDNNs) pres…
Extrinsic Bayesian Optimizations on Manifolds
Yihao Fang, Mu Niu, Pokman Cheung +1
We propose an extrinsic Bayesian optimization (eBO) framework for general optimization problems on manifolds. Bayesian optimization algorithms build a surrogate of the objective fu…
Bayesian community detection for networks with covariates
Luyi Shen, Arash Amini, Nathaniel Josephs +1
The increasing prevalence of network data in a vast variety of fields and the need to extract useful information out of them have spurred fast developments in related models and al…
Bayesian Optimal Two-sample Tests in High-dimension
Kyoungjae Lee, Kisung You, Lizhen Lin
We propose optimal Bayesian two-sample tests for testing equality of high-dimensional mean vectors and covariance matrices between two populations. In many applications including g…
Robustness against Adversarial Attacks in Neural Networks using Incremental Dissipativity
Bernardo Aquino, Arash Rahnama, Peter Seiler +2
Adversarial examples can easily degrade the classification performance in neural networks. Empirical methods for promoting robustness to such examples have been proposed, but often…
Adaptive variational Bayes: Optimality, computation and applications
Ilsang Ohn, Lizhen Lin
In this paper, we explore adaptive inference based on variational Bayes. Although several studies have been conducted to analyze the contraction properties of variational posterior…
A likelihood approach to nonparametric estimation of a singular distribution using deep generative models
Minwoo Chae, Dongha Kim, Yongdai Kim +1
We investigate statistical properties of a likelihood approach to nonparametric estimation of a singular distribution using deep generative models. More specifically, a deep genera…
Neural-PDE: A RNN based neural network for solving time dependent PDEs
Yihao Hu, Tong Zhao, Shixin Xu +2
Partial differential equations (PDEs) play a crucial role in studying a vast number of problems in science and engineering. Numerically solving nonlinear and/or high-dimensional PD…
Optimal Bayesian estimation of Gaussian mixtures with growing number of components
Ilsang Ohn, Lizhen Lin
We study Bayesian estimation of finite mixture models in a general setup where the number of components is unknown and allowed to grow with the sample size. An assumption on growin…
Hypothesis testing for populations of networks
Li Chen, Jie Zhou, Lizhen Lin
It has become an increasingly common practice for scientists in modern science and engineering to collect samples of multiple network data in which a network serves as a basic data…
Hierarchical Stochastic Block Model for Community Detection in Multiplex Networks
Arash A. Amini, Marina S. Paez, Lizhen Lin
Multiplex networks have become increasingly more prevalent in many fields, and have emerged as a powerful tool for modeling the complexity of real networks. There is a critical nee…
Network Distance Based on Laplacian Flows on Graphs
Dianbin Bao, Kisung You, Lizhen Lin
Distance plays a fundamental role in measuring similarity between objects. Various visualization techniques and learning tasks in statistics and machine learning such as shape matc…
Differential Geometry for Model Independent Analysis of Images and Other Non-Euclidean Data: Recent Developments
Rabi Bhattacharya, Lizhen Lin
This article provides an exposition of recent methodologies for nonparametric analysis of digital observations on images and other non-Euclidean objects. Fréchet means of distribut…
Averages of Unlabeled Networks: Geometric Characterization and Asymptotic Behavior
Eric Kolaczyk, Lizhen Lin, Steven Rosenberg +2
It is becoming increasingly common to see large collections of network data objects -- that is, data sets in which a network is viewed as a fundamental unit of observation. As a re…
Scale and curvature effects in principal geodesic analysis
Drew Lazar, Lizhen Lin
There is growing interest in using the close connection between differential geometry and statistics to model smooth manifold-valued data. In particular, much work has been done re…
Robust and Parallel Bayesian Model Selection
Michael Minyi Zhang, Henry Lam, Lizhen Lin
Effective and accurate model selection is an important problem in modern data analysis. One of the major challenges is the computational burden required to handle large data sets t…
Bayesian Sparse Linear Regression with Unknown Symmetric Error
Minwoo Chae, Lizhen Lin, David B. Dunson
We study full Bayesian procedures for sparse linear regression when errors have a symmetric but otherwise unknown distribution. The unknown error distribution is endowed with a sym…